HeaT - you have it right in that time dilation explains the one-way trip. When someone approaches a distant object - let's say 250 light years - at .99c, an observer on Earth would see the trip taking about 252.5 years. However, the Earth observer would also notice that time in the reference frame of the spaceship would be ticking slower by about 1/7th (that is, every 7 seconds on Earth would be one second for the traveler). However, in the reference frame of the traveler, time is ticking normally (in fact, Earth's time is slower), but the distance between Earth and the object has contracted by a factor of 7 (the object is about 35 light years away). In both reference frames the traveler as aged about 35-36 years in the journey.

The difficulty in the twin paradox arises if the traveler turns around and returns to Earth (acceleration). During the turn-around, in the traveler's frame, Earth's clock jumps WAY ahead, and even though it will still tick slower in the traveler's frame, Earth's total elapsed time will be much greater than the traveler in all frames. Google "relativistic rocket" for good explanations of acceleration in relativity.

To clear things up a bit for bobfish - when mass is described as being increased by speed, what is being referred to is not mass as we think of it (quantity of matter), but "relativistic mass," which acts as mass in force/momentum equations and is inversely proportional to acceleration. It's equal to m/sqrt(1-(v/c)^2) where m is the "invariant mass" we all know and love (notice how it increases as v increases). Thus the real equation for total energy (kinetic plus rest) is E = mc^2/sqrt(1-(v/c)^2). When there's no velocity, E = mc^2; as velocity approaches c, E approaches infinity.

One more thing I'd just like to add. All these relativistic effects (mass gain, length contraction, time dilation, etc.) are just that. Relative. If you were in a spaceship with no windows , you'd have no way to tell whether you were traveling .0000000001c or .9999999999c (relative to destination). Without any way to see the universe, you'd have no way of knowing which. Until, of course, you slammed into something and created a blast roughly equivalent to the big bang.

Dont you need infinite energy to accelerate something to the speed of light or more? Not sure where i heard it, but it was a while ago. But it would basically mean for anything to go faster then the speed of light, it would have to destroy the universe.

E=mc^2

where:
E = energy
m = mass
c = speed of light

Correct?

edit: nm read the rest of the thread, but im leaving this here :)

Even if the craft had windows, it would be perfectly valid to surmise that all outside is moving with uniform velocity and that you remain at rest.

@wolfy E=mc^2, doesn't refer to what you want it to. It refers to potential energy of on object capable of being turned into energy via exothermic reaction. It doesn't take much matter to make alot of energy, however it takes alot of energy to make matter.

That would depend upon context. But it is strictly not potential energy in the sense physicists use it, because in special relativity all motion is inertial and thus the potential energy of bodies is zero, because there are no external forces.

The E can be the energy required to create a particle of mass m, say in a one loop diagram, where a mater-antimatter pair is created, but is more often used to refer to the rest energy of a body of rest mass m or kinetic energy of a body of relativistic mass m.

would 'your inertial mass' perhaps be a better way of saying it?

Would you have a higher gravitational pull, or would it just be more difficult to change directions?

I imagine with time dilation, as you pass by a planet, since to you it would seem you are going through the field of gravity for a relatively short time (compared to what the planet sees), that would mean you would experience a disproportionately low deflection due to it, which is consistent with the idea of inertia, but not mass, increasing.

This could all be bullshit, I'm pulling it out my ass every step of the way.

would 'your inertial mass' perhaps be a better way of saying it?

Would you have a higher gravitational pull, or would it just be more difficult to change directions?

I imagine with time dilation, as you pass by a planet, since to you it would seem you are going through the field of gravity for a relatively short time (compared to what the planet sees), that would mean you would experience a disproportionately low deflection due to it, which is consistent with the idea of inertia, but not mass, increasing.

This could all be bullshit, I'm pulling it out my ass every step of the way.

Yes, inertial or relativistic mass (as distinct from rest mass) is clearer and more accurate.

In a way it does increase gravitational "pull", as the body would have a greater kinetic energy.

A particle with mass would have to become massless to achieve c. It's that simple.

We just went over this in class today. Let's start with Newton's 2nd law, F=ma. This can also be written as F=m (dp/dt), which means a force is equal to a rate of change in momentum. To clarify, momentum is mass times velocity, and since a change in velocity is an acceleration, and an acceleration is defined as a rate of change in velocity, so this all makes sense. Now, this equation is not quite correct due to Newton not knowing anything about relativistic effects. In reality force is equal to your rate of change in relativistic momentum. (Note also that when I say "time" or am talking about "rates" I mean from an observer's inertial reference frame, which means that he is not accelerating. The time according to the thing moving really fast is different). But what is your relativistic momentum? It is mass times velocity times the Lorentz factor, γ (gamma), which is (1-(v^2/c^2)^-1/2, where c is the speed of light = 3e8m/s. It can be written simply as Prel= γmv. So we can think of a force as the rate of change of relativistic momentum, or F=d(γmv)/dt. This can also be written F=(γm) dv/dt, or F=γma. This means that your mass is actually γm, which in expanded form is m/(1-(v^2/c^2)^1/2. What happens when you increase v? The quantity (v^2/c^2) approaches 1, so the quantity in the denominator approaches zero, which makes the mass approach infinity as v approaches c. Also, since m increases, the force needed to accelerate it towards c increases until an infinite force is required to get it to c. This also means that an infinite amount of energy is required to move it any sort of distance. (W=Fd).

However, if your mass is zero then you can go the speed of light, which is exactly how light does it. In fact, you'll always be moving at c.

So we can think of a force as the rate of change of relativistic momentum, or F=d(γmv)/dt. This can also be written F=(γm) dv/dt, or F=γma. This means that your mass is actually γm, which in expanded form is m/(1-(v^2/c^2)^1/2.

you have to remember to keep the gamma inside of the derivative since it is time dependent. then m*d(v/(1-(v/c)^2)^1/2)/dt = γ^3ma